Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Given:
[tex]\[ h(x) = 0.000371\left(x^2 - 1280x\right) + 152 \][/tex]

The Golden Gate Bridge is a suspension bridge with two cables hung from two towers of equal height that are 1,280 meters apart. The function models [tex]\( h \)[/tex], the height of each cable above the ground in meters, as it relates to [tex]\( x \)[/tex], the cable's horizontal distance from the left tower in meters. What is the height of the towers in meters?

Choose one answer:
(A) 640
(B) 152
(C) 0.000371
(D) 198

Sagot :

GinnyAnswer
Let's analyze the given function:

[tex]\[ h(x) = 0.000371(x^2 - 1280x) + 152 \][/tex]

This function represents the height [tex]\( h \)[/tex] of the cable above the ground as it relates to [tex]\( x \)[/tex], the horizontal distance from the left tower. To find the height of the towers, we need to determine the height at the point where [tex]\( x = 0 \)[/tex].

Step-by-Step Solution:

1. Substitute [tex]\( x = 0 \)[/tex] into the function:

[tex]\[ h(0) = 0.000371(0^2 - 1280 \times 0) + 152 \][/tex]

2. Simplify the expression inside the parentheses:

[tex]\[ h(0) = 0.000371(0 - 0) + 152 \][/tex]
[tex]\[ h(0) = 0.000371 \times 0 + 152 \][/tex]

3. Since [tex]\( 0.000371 \times 0 = 0 \)[/tex], the equation simplifies to:

[tex]\[ h(0) = 0 + 152 \][/tex]
[tex]\[ h(0) = 152 \][/tex]

Therefore, the height of the towers is [tex]\( 152 \)[/tex] meters.

So the correct answer is:

(B) 152
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.